$A$ $B$ $C$ If: $ AC = 24$, $ AB = 3x + 2$, and $ BC = 4x + 8$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {3x + 2} + {4x + 8} = {24}$ Combine like terms: $ 7x + 10 = {24}$ Subtract $10$ from both sides: $ 7x = 14$ Divide both sides by $7$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $BC$ $ BC = 4({2}) + 8$ Simplify: $ {BC = 8 + 8}$ Simplify to find ${BC}$ : $ {BC = 16}$